Mathematical Modeling and Decomposition of Hydrodynamics-Acoustic Fields Using Perturbation Methods

Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

Conservation of mass, momentum, energy and state equations are recognized as basic mathematical models in the analysis of acoustic behavior of cavitation as well as supercavitation. Also, it is known that the order of acoustics effects aren’t as higher as hydrodynamics ones. Therefore, in this paper, initially, for comparing different terms of equations, via using scale analysis, conservation equations are converted into dimensionless. Then by comparing all conditions coupled with weighting terms available in those equations, groups of parameter which are most appropriate with the hydrodynamics and hydroacoustic of the cavitating flow were selected. By regarding acoustic as lower order phenomenon, compared to hydrodynamic of flow and simultaneously using perturbation method, two equations containing leading and first orders and different terms could be attained. Obtained results were indicated that leading order equations represent hydrodynamic of the cavitating flow and first order equations indicate acoustics of cavitation or supercavitation. Acoustic equations of the present study contain terms related to fluid viscosity, density and pressure changes and background flow velocity. As acoustic equations coupled with leading order equations, in order to find noise of cavitation, equations of fluid flow for compressible flow should be resolved.